| PREFACE
The book is divided into nine chapters. Except for the first two introductory chapters, each chapter is independent and restricted to a particular subject to be studied. To the best of the author s knowledge, the most appropriate theories have been chosen to model the specific topic of VCSELs. In Chapters 3 and 4, theoretical models have been developed to analyze the modal profile and polarization, respectively, of VCSELs. The most popular structure of VCSELs is a cylindrical symmetric cavity, which is assumed in the derivation of the models. In addition, this configuration of VCSELs allows investigation of the modal profile and polarization separately such that the complexity of theoretical models can be reduced. In Chapter 3, different methods of solving the wave equation for the modal profile of VCSELs are discussed in detail. The reader can choose the most appropriate model with the required speed and accuracy to analyze the problems. In Chapter 4, two- and four-level models are described to study the polarization properties of the fundamental transverse mode. These simplified models can evaluate the dominant factors that control the polarization properties of VCSELs. It must be noted that the investigation of VCSELs using cold cavity approximations is not realistic. This is so because most of the measurable data, such as threshold current, lasing wavelength, slope efficiency, and output power, all depend on the operating temperature of lasers. Furthermore, the optical behavior of VCSELs is affected by thermal lensing (i.e., self-focusing of transverse modes into the core region of the active layer). Therefore, the thermal properties of VCSELs are investigated in Chapter 5. The method of effective temperature using a simple rate equation model is presented. Effective thermal conductivity and heat generation rate are also derived. The objective in defining effective temperature is to simplify the study by using a rate equation model so that the computational efficiency can be improved. However, this approach will not provide detailed information on heat distribution. Detailed heat distribution inside the laser cavity is studied by solving the heat equation numerically. In this case, the influence of thermal lensing on the optical field profile can be evaluated. Spatial hole burning of carrier concentration also has significant influence on the modal profile of VCSELs. Therefore, Chapter 6 describes the use of a simple rate equation to evaluate the distribution of carrier concentration inside the active region. In this case, self-consistent calculation of optical gain and carrier concentration (i.e., self-consistent calculation of the Poisson and Schrödinger equations) is ignored to simplify the calculation. Different methods for approximating the nonuniform distribution of carrier concentration are also discussed. On the other hand, nonuniform distributions of electric potential and current are required as the input parameters to calculate the heat distribution inside the laser cavity. They have to be solved numerically using the Poisson and continuity equations simultaneously with appropriate boundary conditions. The electric potential across the active layer and the corresponding carrier concentration can be linked together by a simple diode equation. This is so because the simplified relation between optical gain and carrier concentration has been assumed. The self-consistent calculation of optical field, heat, and electrical characteristics of VCSELs is also described in Chapter 6. The dynamic response of VCSELs is analyzed in Chapter 7. Preliminary investigation of the dynamic response of VCSELs using a simple rate equation model is described. Hence, the time variation of carrier concentration and photon density inside the active layer can be calculated. Furthermore, detailed analysis of optical fields can be considered using the beam propagation method such that the influence of optical confinement on the dynamic response of VCSELs can be evaluated. However, detailed investigation of the transient response of heat and electrical properties is avoided in the self-consistent calculation. This is because the time variation of heat and voltage, which are related to heat and the Poisson equations, is much slower than that of photon density and carrier concentration. This assumption significantly reduces the computation time of the model without sacrificing the accuracy of the calculation. The influence of various transportation mechanisms inside the quantum well (QW) active region on the dynamic response of VCSELs is also discussed in this chapter. The methods used to evaluate the spontaneous emission and linewidth of VCSELs are described in Chapter 8. Simple models have been developed to study these parameters quantitatively through the investigation of the spontaneous emission factor and linewidth enhancement factor. On the other hand, the magnitude of the spontaneous emission factor and linewidth enhancement factor is evaluated using rate equation model by empirically fitting the measurable data. Hence, design criteria to optimize the spontaneous emission of VCSELs are obtained. Other nonlinear features of VCSELs such as self-sustained pulsation, bistability, dual-wavelength operation, and wavelength tunability are studied in Chapter 9 using rate equation models. The advantage of using simple rate equation models is that the parameters that describe the nonlinear behavior of VCSELs can be easily extracted through some measurable data such as injection current and lasing power. In conclusion, this book presents the most effective way to implement laser models of VCSELs, which the reader can easily understand. However, the readers are assumed to have the usual undergraduate background knowledge of electromagnetic theory and solid-state physics as well as basic computational skills. Materials of this research monograph concentrate on the evaluation of modeling techniques to analyze VCSELs under various operating conditions. As each chapter of this book is mostly independent of the other chapters, readers can selectively study any chapter for their own interest. Although this book is of most interest to the design engineer of VCSELs, it also provides valuable information to CAD tool designers in other fields of semiconductor lasers. Siu Fung Yu Singapore |
Design and fabrication of vertical cavity surface emitting lasers (VCSELs) requires an iterative process, which is extremely expensive and time-consuming. The use of computer-aided design (CAD) tools can help shorten the design cycle and speed up the development process. Laser models, which are found in the literature, can be used to implement CAD tools for the analysis and design of VCSELs. However, some comprehensive models, which perform sophisticated functions, are difficult to implement and show low computational efficiency. Other simplified models exhibit high computing speed but deliver inadequate descriptions of the observed effects. As a result, inconsistent conclusions may be obtained because different assumptions are applied. This book attempts to provide a guideline for the derivation of models based on appropriate assumptions for a particular problem so that the phenomena observed by the experiment can be easily explained. In fact, the objective throughout this book is to search for the simplest and most direct treatment for modeling VCSELs. The author believes that the laser models covered in this book can help the readers customize their CAD tools to fit into their applications. In addition, the readers should have no difficulty in implementing their own laser models.
TABLE OF CONTENTS Chapter 9 - Nonlinear Characteristics of Vertical Cavity Surface Emitting Lasers
| CHAPTER 9 Nonlinear Characteristics of Vertical Cavity Surface Emitting Lasers The nonlinear characteristics of single-cavity VCSELs, including self-sustained pulsation and bistability, are studied with the influence of self-focusing and diffraction loss taken into consideration. The effect of diffraction loss on the modulation response of single-cavity VCSELs is also discussed. On the other hand, the conditions of self-sustained pulsation and bistability of coupled cavity VCSELs are investigated. The dual-wavelength operation of coupled-cavity VCSELs is also analyzed. Polarization switching and bistability in single-cavity VCSELs are also discussed. The possibility of using polarization bistability in high-speed optical digital systems is investigated. Methods for achieving wavelength tunability in VCSELs are also studied. 9.1 INTRODUCTION Vertical cavity surface emitting lasers (VCSELs) are rapidly emerging as a stronger competitor over the facet emitting semiconductor laser in becoming the light source in high-speed optical fiber communication systems [1]. This is because of the three obvious advantages of VCSELs: (1) low diverged circular output beam, which enhances the coupling efficiency into an optical fiber even without the use of an objective lens [2]; (2) low production cost due to the possibility of monolithic fabrication processes and wafer scalar testing [2]; and (3) high direct modulation speed [3]. For the application of VCSELs in digital switching systems (i.e., all-optical switching and memory systems) [4], optical disk (CD and DVD) readout devices as well as optical wavelength division-multiplexed networks [5], nonlinear characteristics such as self-sustained pulsation (SSP) [6], bistability [7,8], and multiple and tunability wavelength operations [9] are required. In split-contact facet emitting lasers, the generation of SSP and optical bistability has been demonstrated [10]. The excitation of SSP and optical bistability is reproducible and is dependent on the negative differential resistance of the saturable absorber. In addition, it is found that facet emitting lasers with narrow stripe width support SSP, due to an unpumped saturable absorption region [11]. Therefore, it is expected that VCSELs with similar configurations can realize SSP and optical bistability. In fact, it is shown that coupled cavity VCSELs with an intracavity absorber demonstrate SSP and optical bistability [12]. These nonlinear characteristics are due to the negative differential resistance of the saturable absorber, which can be controlled by an electrical bias. On the other hand, it is believed that single-cavity VCSELs of small cavity size (e.g., those with selective oxidization, proton, or ion implantation configuration) support SSP because of the excessive saturable absorption of the unpumped region. However, no strong signal of SSP has been observed experimentally [6]. Therefore, it is usually recognized that output characteristics of single-cavity VCSELs are more stable than those of facet emitting lasers, especially under the influence of external optical feedback [13,14]. The suppression of SSP in single-cavity VCSELs has been explained by the influence of diffraction loss, which dominates over the saturable absorption [15]. Hence, large saturable absorption is not the sufficient requirement to generate SSP in single-cavity VCSELs with small cavity size. In order to utilize VCSELs with single and coupled cavities in high-speed digital systems, the generation conditions of SSP and optical bistability must be determined. Dual-wavelength laser sources are desirable in several applications such as two-wavelength interferometry for distance measurement, terahertz difference signal generation, and frequency mixing. An optimal source for these applications would be a single-diode laser capable of simultaneous coaxial emission at two different wavelengths. It is noted that cleaved coupled cavity (C3) facet emitting semiconductor lasers could give rise to dual-wavelength emission [16]. On the other hand, two monolithic cavities, one grown on top of the other and sharing a common mirror form coupled cavity VCSELs, which are believed to give better performance than C3 facet emitting lasers. This is because the coupled dual-wavelength emissions of the coupled cavity VCSELs are widely spaced (i.e., ∼13 nm), and have the same threshold under optical pumping [17]. Therefore, it is interesting to further investigate the lasing characteristics of coupled cavity VCSELs with various configurations. In Chapter 4, the polarization stability of single-cavity VCSELs under the influence of an injection current has been discussed. In the analysis, the influence of gain anisotropy and birefringence on the selection mechanism of the two orthogonal polarized modes has been studied. In this chapter, the switching mechanisms of the two orthogonal polarized modes under the trigger of external optical injection are analyzed [18]. The influence of self-heating and longitudinal distribution of optical field is also considered. It is interesting to study the fast switching characteristic of the two orthogonal polarized modes by external optical triggering as this behavior has significant potential in the application of all-optical switching and optical memory [4]. Tunable lasers are used in spectroscopy, beam steering, wavelength-division multiplexing, interferometry, and a wide variety of other applications [4]. In facet emitting semiconductor lasers, the continuous tuning of the wavelength is realized by using diffraction grating and bulk optics to form an external cavity [19]. However, an integrated and continuously tunable laser is far more desirable and potentially cost-effective. In this chapter, the possibility of utilizing VCSELs as continuously tunable wavelength lasers is discussed. This chapter is organized as follows. First, SSP and optical bistability of single-cavity VCSELs are discussed and analyzed. The conditions of SSP and optical bistability are derived, including calculation of self-focusing and diffraction loss. It is found that the conditions of optical bistability, which are similar to those of facet emitting lasers, are dependent on the carrier lifetime and differential gain between the regions of gain and saturable absorption. However, the conditions of SSP in VCSELs are different from those of facet emitting lasers because of the presence of diffraction loss. In addition, the influence of diffraction loss on the modulation response of VCSELs is studied. Then, SSP and optical bistability of coupled cavity VCSELs with an intracavity absorber are investigated. The corresponding conditions of SSP and optical bistability are also derived. On the other hand, the dual wavelength emission of coupled cavity VCSELs with two active cavities is discussed and analyzed. Different approaches to realizing polarization switching and bistable operation in single-cavity VCSELs are then studied. A theoretical model is developed to analyze the switching of the two orthogonal polarized modes under the trigger of external optical injection. Finally, design considerations of tunable wavelength single-cavity VCSELs are discussed. |
